# GATE | GATE-CS-2015 (Set 2) | Question 51

The secant method is used to find the root of an equation f(x) = 0. It is started from two distinct estimates xa and xb for the root. It is an iterative procedure involving linear interpolation to a root. The iteration stops if f(xb) is very small and then xb is the solution. The procedure is given below. Observe that there is an expression which is missing and is marked by? Which is the suitable expression that is to be put in place of? So that it follows all steps of the secant method?

Secant

```Initialize: xa, xb, ε, N     // ε = convergence indicator
fb = f(xb) i = 0
while (i < N and |fb| > ε) do
i = i + 1                 // update counter
xt = ?                    // missing expression for
// intermediate value
xa = xb                   // reset xa
xb = xt                   // reset xb
fb = f(xb)                // function value at new xb
end while
if |fb| > ε
then // loop is terminated with i = N
write “Non-convergence”
else
write “return xb”
end if ```

(A) xb – (fb– f(xa)) fb/ (xb – xa)
(B) xa– (fa– f(xa)) fa/ (xb – xa)
(C) xb – (fb – xa) fb/ (xb – fb(xa)
(D) xa – (xb – xa) fa/ (fb – f(xa))